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25,300 | While adding phase shifting to three-level converters improves harmonic performance, it comes at the cost of adding 2,3, or even 4 additional STATCOMs. It also adds little too no redundancy, as the switching pattern is too complex to accommodate the loss of one STATCOM. As the idea of the three-level converter is to ad... | Static synchronous compensator | 0.807712 |
25,301 | Adding additional levels to a converter topology has the benefit of more closely mirroring a true voltage sine wave, which reduces harmonic generation and improves performance. If all three phases of a VSC utilize its own two-level converter topology, the phase-to-phase voltage will be three levels (as while the three ... | Static synchronous compensator | 0.807712 |
25,302 | Since a STATCOM varies its voltage magnitude to control reactive power, the topology of how the VSC is designed and connected defines how effectively and quickly it can operate. There are numerous different topologies available for VSCs and power electronic based converters, the most common ones are covered below. IGBT... | Static synchronous compensator | 0.807712 |
25,303 | Watching the timetable and moderating the discussion is entrusted to the chairperson.The first few Physics Fights of the tournament are selective fights. Each team meets different competitors at random. Depending on the number of battles won and the number of points obtained, each team gets its rating, and the nine top... | Ukrainian Physicists' Tournament for University Students | 0.80771 |
25,304 | Then the teams come together for the final stage of the tournament, and present their solutions in the format of Physics Fights. During a Physics Fight each team consequently acts as a reporter, an opponent and a reviewer. The opponent challenges the reporter for one of the problems. | Ukrainian Physicists' Tournament for University Students | 0.80771 |
25,305 | Ukrainian Physicists' Tournament for University Students (Ukrainian: Всеукраїнський студентський турнір фізиків, commonly abbreviated as СТФ) is a creative team competition of university students targeted to realize their potential through solving complicated scientific problems and defending their research projects in... | Ukrainian Physicists' Tournament for University Students | 0.80771 |
25,306 | The pure solid crystals are then separated from the remaining liquor by filtration or centrifugation. Recrystallization: In analytical and synthetic chemistry work, purchased reagents of doubtful purity may be recrystallised, e.g. dissolved in a very pure solvent, and then crystallized, and the crystals recovered, in o... | List of purification methods in chemistry | 0.807707 |
25,307 | Like Plato, Aristotle believed in an eternal cosmos with no beginning and no end (which in turn follows Parmenides' famous statement that "nothing comes from nothing"). In what he called "first philosophy" or metaphysics, Aristotle did intend a theological correspondence between the prime mover and a deity; functionall... | Argument from motion | 0.807706 |
25,308 | Aristotle argued against the idea of a first cause, often confused with the idea of a "prime mover" or "unmoved mover" (πρῶτον κινοῦν ἀκίνητον or primus motor) in his Physics and Metaphysics. Aristotle argued in favor of the idea of several unmoved movers, one powering each celestial sphere, which he believed lived bey... | Argument from motion | 0.807706 |
25,309 | A propagation cycle is not initiated because each growth step requires the assistance of light.Photopolymerization can be used as a photographic or printing process because polymerization only occurs in regions which have been exposed to light. Unreacted monomer can be removed from unexposed regions, leaving a relief p... | Polymerization | 0.807705 |
25,310 | In chemistry, the oxidation state, or oxidation number, is the hypothetical charge of an atom if all of its bonds to other atoms were fully ionic. It describes the degree of oxidation (loss of electrons) of an atom in a chemical compound. Conceptually, the oxidation state may be positive, negative or zero. While fully ... | Oxidation states | 0.807696 |
25,311 | Introductory chemistry uses postulates: the oxidation state for an element in a chemical formula is calculated from the overall charge and postulated oxidation states for all the other atoms. A simple example is based on two postulates, OS = +1 for hydrogen OS = −2 for oxygenwhere OS stands for oxidation state. This ap... | Oxidation states | 0.807696 |
25,312 | On November 7, 2016 an event was held in Brussels, organized by MEP Marietje Schaake in the European Parliament and described by danah Boyd. Only eleven days later at New York University there was a conference on "Fairness, Accountability, and Transparency in Machine Learning " where Principles for Accountable Algorith... | Data portability | 0.807696 |
25,313 | Almost two years later a paper appeared that challenges earlier papers, especially Wachter / Mittelstadt / Floridi.On both sides of the Atlantic there has been recent activity pertaining to this ongoing debate. Early in 2016 experts on artificial intelligence and UK government officials met during a number of meetings,... | Data portability | 0.807696 |
25,314 | of 2016, and other notable ones were by Joshua Kroll and Mireille Hildebrandt.Another 2016 paper, this one published by Katarinou et al., includes remarks on a right of appeal such that "individuals would have a right to appeal to a machine against a decision made by a human. "A third 2016 paper, one co-authored by Mit... | Data portability | 0.807696 |
25,315 | Such a right was included in the EU Data Protection Directive of 1995, but not much enforcement followed. An article in Wired emphasised the poignancy of the discussion. The issue has been discussed by Bygrave, and by Hildebrandt, who claimed this to be one of the most important transparency rights in the era of machin... | Data portability | 0.807696 |
25,316 | Examples of radical SAM enzymes include spore photoproduct lyase, activases of pyruvate formate lyase and anaerobic sulfatases, lysine 2,3-aminomutase, and various enzymes of cofactor biosynthesis, peptide modification, metalloprotein cluster formation, tRNA modification, lipid metabolism, etc. Some radical SAM enzymes... | S-Adenosyl methionine | 0.807695 |
25,317 | For detection and quantification tasks, so-called observer models have been thoroughly studied and validated against human observers, and a range of spatial-domain models exist in the literature. Image interpretation based on deep learning and artificial intelligence (AI) is an active research field, and might become a... | In silico clinical trials | 0.807685 |
25,318 | An in silico clinical trial, also known as a virtual clinical trial, is an individualized computer simulation used in the development or regulatory evaluation of a medicinal product, device, or intervention. While completely simulated clinical trials are not feasible with current technology and understanding of biology... | In silico clinical trials | 0.807685 |
25,319 | In statistics, a truly random sample means selecting individuals from a population with an equivalent probability; in other words, picking individuals from a group without bias. Failing to do this correctly will result in a sampling bias, which can dramatically increase the sample error in a systematic way. For example... | Sampling variance | 0.807683 |
25,320 | This boundary layer is approximately 0.3 nm thick. Within this short distance, the water concentration drops from 2M on the headgroup side to nearly zero on the tail (core) side. The hydrophobic core of the bilayer is typically 3-4 nm thick, but this value varies with chain length and chemistry. Core thickness also var... | Lipid membranes | 0.807681 |
25,321 | Lipid bilayers can be created artificially in the lab to allow researchers to perform experiments that cannot be done with natural bilayers. They can also be used in the field of Synthetic Biology, to define the boundaries of artificial cells. These synthetic systems are called model lipid bilayers. | Lipid membranes | 0.807681 |
25,322 | Xenetic Biosciences (London, Great Britain) is a leading biopharmaceutical company operating from the UK that develops high-value, differentiated pharmaceutical products in the fields of protein drugs, vaccines and anti-cancer drugs. SymBioTec GmbH (Saarbrücken, Germany) is a company working to develop next generation ... | SynBio | 0.80768 |
25,323 | The project is a significant example of international cooperation between researchers in Russia, England, and Germany. Special project company SynBio LLC is headquartered in Moscow.Currently, SynBio LLC is developing nine drugs based on three biotechnology platforms (Histone, PolyXen and Gemacell) for the treatment of ... | SynBio | 0.80768 |
25,324 | A domestic supply typically consists of a large cable connected to a service head, the sealed box containing the main supply fuse, treated as the supply to the premises. This will typically have a value from 40–100 A. Separate line and neutral cables (tails) go from here to an electricity meter. More tails proceed from... | Radial circuit | 0.80768 |
25,325 | In mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function. In other words, a transcendental function "transcends" algebra in that it cannot be expressed algebraically using a finite amount of terms. Examples of transcendental func... | Transcendental functions | 0.807679 |
25,326 | Formally, an analytic function f (z) of one real or complex variable z is transcendental if it is algebraically independent of that variable. This can be extended to functions of several variables. | Transcendental functions | 0.807678 |
25,327 | Most familiar transcendental functions, including the special functions of mathematical physics, are solutions of algebraic differential equations. Those that are not, such as the gamma and the zeta functions, are called transcendentally transcendental or hypertranscendental functions. | Transcendental functions | 0.807678 |
25,328 | In particle physics, the quantum yield (denoted Φ) of a radiation-induced process is the number of times a specific event occurs per photon absorbed by the system. | Quantum yield | 0.807676 |
25,329 | A major benefit of systolic arrays is that all operand data and partial results are stored within (passing through) the processor array. There is no need to access external buses, main memory or internal caches during each operation as is the case with Von Neumann or Harvard sequential machines. The sequential limits o... | Systolic array | 0.807676 |
25,330 | Cisco PXF network processor is internally organized as systolic array. Google’s TPU is also designed around a systolic array. Paracel FDF4T TestFinder text search system Paracel FDF4G GeneMatcher Biological (DNA and Protein) search system Inferentia chip at Amazon Web Services MIT Eyeriss is a systolic array accelerato... | Systolic array | 0.807676 |
25,331 | At this point, the result of the multiplication is stored in the array and can now be output a row or a column at a time, flowing down or across the array.Systolic arrays are arrays of DPUs which are connected to a small number of nearest neighbour DPUs in a mesh-like topology. DPUs perform a sequence of operations on ... | Systolic array | 0.807676 |
25,332 | In parallel computer architectures, a systolic array is a homogeneous network of tightly coupled data processing units (DPUs) called cells or nodes. Each node or DPU independently computes a partial result as a function of the data received from its upstream neighbours, stores the result within itself and passes it dow... | Systolic array | 0.807676 |
25,333 | There is time-use research and research on various types of media uses on cognition. Impacts of screen time as well as play behavior on cognition may depend heavily on the activities, contexts, substituted activities and contents. (see also Reality#Media and below) Motivations to make use of pharmacological cognitive e... | Cognitive enhancement | 0.807675 |
25,334 | Development of education may also be part of neuroenhancement. Results in neuroscience and software – e.g. AI and adaptive online learning environments – can be relevant to this development. Lifelong learning may be considered a way of cognitive enhancement. For the scope of neuroenhancement relating to education and w... | Cognitive enhancement | 0.807675 |
25,335 | Modafinil has replaced dextroamphetamine in certain types of military operations due to its superior side effects profile. development of more adequate tests, evaluations or measures about positive effects A study notes that there is a problem of "how to define cognition and whether or not it can be understood in simpl... | Cognitive enhancement | 0.807675 |
25,336 | Neuroenhancement or cognitive enhancement refers to the targeted enhancement and extension of cognitive and affective abilities based on an understanding of their underlying neurobiology in healthy persons who do not have any mental illness and outcomes in experimental research. As such, it can be thought of as an umbr... | Cognitive enhancement | 0.807675 |
25,337 | Several methods rely on a standard candle, which is an astronomical object that has a known luminosity. The ladder analogy arises because no single technique can measure distances at all ranges encountered in astronomy. Instead, one method can be used to measure nearby distances, a second can be used to measure nearby ... | Stellar distance | 0.807674 |
25,338 | This journal began as "Physical Review" in 1893. In 1913 the American Physical Society took over Physical Review. In 1970 Physical Review was subdivided into Physical Review A, B, C, and D. From 1990 until 1993 a process was underway which split the journal then entitled Physical Review A: General Physics into two jour... | Physical Review E | 0.807673 |
25,339 | Although the focus of this journal is many-body phenomena, the broad scope of the journal includes quantum chaos, soft matter physics, classical chaos, biological physics and granular materials. Also emphasized are statistical physics, equilibrium and transport properties of fluids, liquid crystals, complex fluids, pol... | Physical Review E | 0.807673 |
25,340 | Physical Review E is indexed in the following bibliographic databases: Science Citation Index Expanded Current Contents / Physical, Chemical & Earth Sciences Chemical Abstracts Service - CASSI Current Physics Index Inspec MEDLINE Index Medicus PubMed NLM catalog Physics Abstracts SPIN | Physical Review E | 0.807673 |
25,341 | As the name implies, deductive languages are rooted in the principles of deductive reasoning; making inferences based upon current knowledge. The first recommendation to use a clausal form of logic for representing computer programs was made by Cordell Green (1969) at Stanford Research Institute (now SRI International)... | Deductive language | 0.807672 |
25,342 | As new facts are established or added, they form the basis for new inferences. As the core of early expert systems, artificial intelligence systems which can make decisions like an expert human, knowledge bases provided more information than databases. They contained structured data, with classes, subclasses, and insta... | Deductive language | 0.807672 |
25,343 | In organic chemistry, an amino sugar (or more technically a 2-amino-2-deoxysugar) is a sugar molecule in which a hydroxyl group has been replaced with an amine group. More than 60 amino sugars are known, with one of the most abundant being N-Acetyl-d-glucosamine, which is the main component of chitin. Derivatives of am... | Amino sugars metabolism | 0.807671 |
25,344 | TE buffer is a commonly used buffer solution in molecular biology, especially in procedures involving DNA, cDNA or RNA. "TE" is derived from its components: Tris, a common pH buffer, and EDTA, a molecule that chelates cations like Mg2+. The purpose of TE buffer is to solubilize DNA or RNA, while protecting it from degr... | TE buffer | 0.807668 |
25,345 | ChemInform was an indexing and abstracting service and database in chemistry. The service published abstracts related to organic, organometallic, inorganic and physical chemistry. | ChemInform | 0.807668 |
25,346 | The abstracts were published in ChemInform: Selected Abstracts in Chemistry from 1970 to 2016. It was originally published in two parts as Chemischer Informationsdienst: anorganische und physikalische Chemie and Chemischer Informationsdienst: organische Chemie, which merged in 1972 into the single Chemischer Informatio... | ChemInform | 0.807668 |
25,347 | In mathematics, specifically algebraic topology, the mapping cylinder of a continuous function f {\displaystyle f} between topological spaces X {\displaystyle X} and Y {\displaystyle Y} is the quotient M f = ( ( × X ) ⨿ Y ) / ∼ {\displaystyle M_{f}=((\times X)\amalg Y)\,/\,\sim } where the ⨿ {\displaystyle \amalg } de... | Mapping cylinder | 0.807667 |
25,348 | Mapping cylinders are quite common homotopical tools. One use of mapping cylinders is to apply theorems concerning inclusions of spaces to general maps, which might not be injective. Consequently, theorems or techniques (such as homology, cohomology or homotopy theory) which are only dependent on the homotopy class of ... | Mapping cylinder | 0.807667 |
25,349 | An excellent example of transgenic modification is in the case of cold resistant strawberries. In one particular variety genes from the arctic flounder, a fish that lives in very cold water, were used to give plants resistance to cold. This modification works because of the genetics of the arctic flounder. | Breeding of strawberries | 0.807666 |
25,350 | Molecular breeding is the application of molecular biology tools in a breeding program. | Breeding of strawberries | 0.807666 |
25,351 | Changes in thermodynamic conditions make it favourable for mineral assemblages to react with each other to produce new minerals; as such, it is possible for two rocks to have an identical or a very similar bulk rock chemistry without having a similar mineralogy. This process of mineralogical alteration is related to th... | Mineral identification | 0.807666 |
25,352 | Oxygen and silicon are by far the two most important – oxygen composes 47% of the crust by weight, and silicon accounts for 28%.The minerals that form are those that are most stable at the temperature and pressure of formation, within the limits imposed by the bulk chemistry of the parent body. For example, in most ign... | Mineral identification | 0.807666 |
25,353 | The abundance and diversity of minerals is controlled directly by their chemistry, in turn dependent on elemental abundances in the Earth. The majority of minerals observed are derived from the Earth's crust. Eight elements account for most of the key components of minerals, due to their abundance in the crust. These e... | Mineral identification | 0.807666 |
25,354 | The notation and terminology are relatively obsolete today. Its uses in physics include continuum mechanics and electromagnetism. In this article, upper-case bold variables denote dyadics (including dyads) whereas lower-case bold variables denote vectors. An alternative notation uses respectively double and single over... | Dyadics | 0.807663 |
25,355 | The formalism of dyadic algebra is an extension of vector algebra to include the dyadic product of vectors. The dyadic product is also associative with the dot and cross products with other vectors, which allows the dot, cross, and dyadic products to be combined to obtain other scalars, vectors, or dyadics. It also has... | Dyadics | 0.807663 |
25,356 | In mathematics, specifically multilinear algebra, a dyadic or dyadic tensor is a second order tensor, written in a notation that fits in with vector algebra. There are numerous ways to multiply two Euclidean vectors. The dot product takes in two vectors and returns a scalar, while the cross product returns a pseudovect... | Dyadics | 0.807663 |
25,357 | These results have led to a sub-field within computer vision where artificial systems are designed to mimic the processing and behavior of biological systems at different levels of complexity. Also, some of the learning-based methods developed within computer vision (e.g. neural net and deep learning based image and fe... | Applications of computer vision | 0.807663 |
25,358 | Neurobiology has greatly influenced the development of computer vision algorithms. Over the last century, there has been an extensive study of eyes, neurons, and brain structures devoted to the processing visual stimuli in both humans and various animals. This has led to a coarse, yet convoluted, description of how nat... | Applications of computer vision | 0.807663 |
25,359 | A second application area in computer vision is in industry, sometimes called machine vision, where information is extracted for the purpose of supporting a production process. One example is quality control where details or final products are being automatically inspected in order to find defects. One of the most prev... | Applications of computer vision | 0.807663 |
25,360 | Another application is to use computer vision to extract data from surgical video films. Deep learning processes information through networks of multiple neuron layers, which allows computers to learn complex tasks. One common neuronal arrangement, the convolutional neural networks (CNNs), has a structure similar to a ... | Applications of computer vision | 0.807663 |
25,361 | One of the most prominent application fields is medical computer vision, or medical image processing, characterized by the extraction of information from image data to diagnose a patient. An example of this is the detection of tumours, arteriosclerosis or other malign changes, and a variety of dental pathologies; measu... | Applications of computer vision | 0.807663 |
25,362 | Some strands of computer vision research are closely related to the study of biological vision—indeed, just as many strands of AI research are closely tied with research into human intelligence, and the use of stored knowledge to interpret, integrate and utilize visual information. The field of biological vision studie... | Applications of computer vision | 0.807663 |
25,363 | In psychophysics, Korte's third law of apparent motion is an observation relating the phenomenon of apparent motion to the distance and duration between two successively presented stimuli. | Korte's third law of apparent motion | 0.807662 |
25,364 | The ϕ4 theory, QED, QCD, as well as the whole Standard Model all assume a (3+1)-dimensional Minkowski space (3 spatial and 1 time dimensions) as the background on which the quantum fields are defined. However, QFT a priori imposes no restriction on the number of dimensions nor the geometry of spacetime. In condensed ma... | The problem of infinities | 0.80766 |
25,365 | The number of broken symmetries is their difference, N − 1, which corresponds to the N − 1 massless fields πk. : 351 On the other hand, when a gauge (as opposed to global) symmetry is spontaneously broken, the resulting Goldstone boson is "eaten" by the corresponding gauge boson by becoming an additional degree of free... | The problem of infinities | 0.80766 |
25,366 | The larger symmetry before spontaneous symmetry breaking is said to be "hidden" or spontaneously broken. : 349–350 Goldstone's theorem states that under spontaneous symmetry breaking, every broken continuous global symmetry leads to a massless field called the Goldstone boson. In the above example, O(N) has N(N − 1)/2 ... | The problem of infinities | 0.80766 |
25,367 | There are different types of degree for different types of maps: e.g. for maps between Banach spaces there is the Brouwer degree in Rn, the Leray-Schauder degree for compact mappings in normed spaces, the coincidence degree and various other types. There is also a degree for continuous maps between manifolds. Topologic... | Topological degree theory | 0.807654 |
25,368 | Two smooth cubic surfaces are isomorphic as algebraic varieties if and only if they are equivalent by some linear automorphism of P 3 {\displaystyle \mathbf {P} ^{3}} . Geometric invariant theory gives a moduli space of cubic surfaces, with one point for each isomorphism class of smooth cubic surfaces. This moduli spac... | Cubic surface | 0.807653 |
25,369 | The lines on a cubic surface X over an algebraically closed field can be described intrinsically, without reference to the embedding of X in P 3 {\displaystyle \mathbf {P} ^{3}}: they are exactly the (−1)-curves on X, meaning the curves isomorphic to P 1 {\displaystyle \mathbf {P} ^{1}} that have self-intersection −1. ... | Cubic surface | 0.807653 |
25,370 | In contrast to the complex case, the space of smooth cubic surfaces over the real numbers is not connected in the classical topology (based on the topology of R). Its connected components (in other words, the classification of smooth real cubic surfaces up to isotopy) were determined by Ludwig Schläfli (1863), Felix Kl... | Cubic surface | 0.807653 |
25,371 | A smooth cubic surface X over a field k which is not algebraically closed need not be rational over k. As an extreme case, there are smooth cubic surfaces over the rational numbers Q (or the p-adic numbers Q p {\displaystyle \mathbf {Q} _{p}} ) with no rational points, in which case X is certainly not rational. If X(k)... | Cubic surface | 0.807653 |
25,372 | In mathematics, a cubic surface is a surface in 3-dimensional space defined by one polynomial equation of degree 3. Cubic surfaces are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than affine space, and so cubic surfaces are generally considered in projectiv... | Cubic surface | 0.807653 |
25,373 | In this respect, cubic surfaces are much simpler than smooth surfaces of degree at least 4 in P 3 {\displaystyle \mathbf {P} ^{3}} , which are never rational. In characteristic zero, smooth surfaces of degree at least 4 in P 3 {\displaystyle \mathbf {P} ^{3}} are not even uniruled.More strongly, Clebsch showed that eve... | Cubic surface | 0.807653 |
25,374 | A central feature of smooth cubic surfaces X over an algebraically closed field is that they are all rational, as shown by Alfred Clebsch in 1866. That is, there is a one-to-one correspondence defined by rational functions between the projective plane P 2 {\displaystyle \mathbf {P} ^{2}} minus a lower-dimensional subse... | Cubic surface | 0.807653 |
25,375 | This is one of many ADE classifications in mathematics. Pursuing these analogies, Vera Serganova and Alexei Skorobogatov gave a direct geometric relation between cubic surfaces and the Lie group E 6 {\displaystyle E_{6}} .In physics, the 27 lines can be identified with the 27 possible charges of M-theory on a six-dimen... | Cubic surface | 0.807653 |
25,376 | This is a distinctive feature of cubics: a smooth quadric (degree 2) surface is covered by a continuous family of lines, while most surfaces of degree at least 4 in P 3 {\displaystyle \mathbf {P} ^{3}} contain no lines. Another useful technique for finding the 27 lines involves Schubert calculus which computes the numb... | Cubic surface | 0.807653 |
25,377 | Most proofs of rationality for cubic surfaces start by finding a line on the surface. (In the context of projective geometry, a line in P 3 {\displaystyle \mathbf {P} ^{3}} is isomorphic to P 1 {\displaystyle \mathbf {P} ^{1}} .) More precisely, Arthur Cayley and George Salmon showed in 1849 that every smooth cubic sur... | Cubic surface | 0.807653 |
25,378 | Magnetically-controlled shunt reactors are intended for automatic control over reactive power and stabilization of voltage levels; these ensure the following: Elimination of daily and seasonal voltage variations in the power network; Improvement of electric power quality; Optimization and automation of power network op... | Controlled shunt reactor | 0.807651 |
25,379 | Tarski's notion of a relation algebra can be defined as a residuated Boolean algebra having an operation x˘ satisfying these two equations. The cancellation step in the above is not possible for Example 3, which therefore is not a relation algebra, x˘ being uniquely determined as x▷I. Consequences of this axiomatizatio... | Residuated Boolean algebra | 0.807647 |
25,380 | The right residual R\S is defined by x(R\S)y if and only if for all z in X, zRx implies zSy. Dually the left residual S/R is defined by y(S/R)x if and only if for all z in X, xRz implies ySz. The power set 2Σ* made a Boolean algebra as for Example 2, but with language concatenation for the monoid. Here the set Σ is use... | Residuated Boolean algebra | 0.807647 |
25,381 | The axiom it fails is x•I = x = I•x, for want of a suitable value for I. Hence conjunction is the only binary Boolean operation making the monoid multiplication that of a residuated Boolean algebra. The power set 2X2 made a Boolean algebra as usual with ∩, ∪ and complement relative to X2, and made a monoid with relatio... | Residuated Boolean algebra | 0.807647 |
25,382 | Any Boolean algebra, with the monoid multiplication • taken to be conjunction and both residuals taken to be material implication x→y. Of the remaining 15 binary Boolean operations that might be considered in place of conjunction for the monoid multiplication, only five meet the monotonicity requirement, namely 0, 1, x... | Residuated Boolean algebra | 0.807647 |
25,383 | A residuated Boolean algebra is an algebraic structure (L, ∧, ∨, ¬, 0, 1, •, I, \, /) such that An equivalent signature better suited to the relation algebra application is (L, ∧, ∨, ¬, 0, 1, •, I, ▷, ◁) where the unary operations x\ and x▷ are intertranslatable in the manner of De Morgan's laws via x\y = ¬(x▷¬y), x▷y ... | Residuated Boolean algebra | 0.807647 |
25,384 | Likewise ◁y is the conjugate of •y. Unlike residuals, conjugacy is an equivalence relation between operations: if f is the conjugate of g then g is also the conjugate of f, i.e. the conjugate of the conjugate of f is f. Another advantage of conjugacy is that it becomes unnecessary to speak of right and left conjugates,... | Residuated Boolean algebra | 0.807647 |
25,385 | The De Morgan duals ▷ and ◁ of residuation arise as follows. Among residuated lattices, Boolean algebras are special by virtue of having a complementation operation ¬. This permits an alternative expression of the three inequalities y ≤ x\z ⇔ x•y ≤ z ⇔ x ≤ z/yin the axiomatization of the two residuals in terms of disjo... | Residuated Boolean algebra | 0.807647 |
25,386 | In mathematics, a residuated Boolean algebra is a residuated lattice whose lattice structure is that of a Boolean algebra. Examples include Boolean algebras with the monoid taken to be conjunction, the set of all formal languages over a given alphabet Σ under concatenation, the set of all binary relations on a given se... | Residuated Boolean algebra | 0.807647 |
25,387 | Telomeres form the terminal region of mammalian chromosomes and are essential for stability and aging and play central roles in diseases such as cancer. Telomeres have been long considered transcriptionally inert DNA-protein complexes until it was shown in the late 2000s that telomeric repeats may be transcribed as tel... | Long non-coding RNA | 0.807647 |
25,388 | Newton's diagram (also known as Newton's parallelogram, after Isaac Newton) is a technique for determining the shape of an algebraic curve close to and far away from the origin. It consists of plotting (α, β) for each term Axαyβ in the equation of the curve. The resulting diagram is then analyzed to produce information... | Curve sketching | 0.807647 |
25,389 | If the sum of the degrees of x and y in each term is always even or always odd, then the curve is symmetric about the origin and the origin is called a center of the curve. Determine any bounds on the values of x and y. If the curve passes through the origin then determine the tangent lines there. For algebraic curves,... | Curve sketching | 0.807647 |
25,390 | In geometry, curve sketching (or curve tracing) are techniques for producing a rough idea of overall shape of a plane curve given its equation, without computing the large numbers of points required for a detailed plot. It is an application of the theory of curves to find their main features. | Curve sketching | 0.807647 |
25,391 | Curry's paradox may be expressed in untyped lambda calculus, enriched by restricted minimal logic. To cope with the lambda calculus's syntactic restrictions, m {\displaystyle m} shall denote the implication function taking two parameters, that is, the lambda term ( ( m A ) B ) {\displaystyle ((mA)B)} shall be equivalen... | Curry's paradox | 0.807647 |
25,392 | Curry's paradox may also be expressed in combinatory logic, which has equivalent expressive power to lambda calculus. Any lambda expression may be translated into combinatory logic, so a translation of the implementation of Curry's paradox in lambda calculus would suffice. The above term X {\displaystyle X} translates ... | Curry's paradox | 0.807647 |
25,393 | Mathematical logic generally does not allow explicit reference to its own sentences. However the heart of Gödel's incompleteness theorems is the observation that a different form of self-reference can be added; see Gödel number. The axiom of unrestricted comprehension adds the ability to construct a recursive definitio... | Curry's paradox | 0.807647 |
25,394 | The argument in formal logic starts with assuming the validity of naming (X → Y) as X. However, this is not a valid starting point. First we must deduce the validity of the naming. The following theorem is easily proved and represents such a naming: In the above statement the formula A is named as X. Now attempt to ins... | Curry's paradox | 0.807647 |
25,395 | The Fermi Gamma-ray Space Telescope (FGST, also FGRST), formerly called the Gamma-ray Large Area Space Telescope (GLAST), is a space observatory being used to perform gamma-ray astronomy observations from low Earth orbit. Its main instrument is the Large Area Telescope (LAT), with which astronomers mostly intend to per... | Fermi LAT | 0.807646 |
25,396 | NASA's Alan Stern, associate administrator for Science at NASA Headquarters, launched a public competition 7 February 2008, closing 31 March 2008, to rename GLAST in a way that would "capture the excitement of GLAST's mission and call attention to gamma-ray and high-energy astronomy ... something memorable to commemora... | Fermi LAT | 0.807646 |
25,397 | The process of dispersal of aerobiological particles has 3 steps: removal from source, dispersion through air, and deposition to rest. The particle geometry and environment affect all three phases, however once it is aerosolized, its fate depends on the laws of physics governing the motion of the air. | Aerobiology | 0.807645 |
25,398 | Once released from rest, the aeroplankton is at the mercy of the wind and physics. The settling speed of spores and pollen vary and is a major factor in dispersion; the longer the particle is floating, the longer it can be caught by a turbulent wind gust. Wind speed and direction fluctuate with time and height, so the ... | Aerobiology | 0.807645 |
25,399 | This means that aeroplankton are everywhere and have been everywhere, and it solely depends on environmental factors to determine which remain. Aeroplankton are found in significant quantities even in the Atmospheric boundary layer (ABL). The effects on climate and cloud chemistry of these atmospheric populations is st... | Aerobiology | 0.807645 |
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